lean_workbook_plus_7629

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

For $a, b, c, d > 0$ real numbers prove that: $(a+b+c+d) \cdot (ab+ac+ad+bc+bd+cd) \ge 6 (abc+bcd+cda+dab) \ \ ; (1)$

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_7629 (a b c d : ℝ) (ha : 0 < a) (hb : 0 < b) (hc : 0 < c) (hd : 0 < d) : (a + b + c + d) * (a * b + a * c + a * d + b * c + b * d + c * d) ≥ 6 * (a * b * c + b * c * d + c * d * a + d * a * b)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph